Question

一个“幸运”年份是指至少有一个日期按“月/日/年”的形式书写时，满足月份数乘以日期数等于年份的最后两位。例如， $1956$ 是幸运年份，因为日期 $7/8/56$ 满足 $7 \times 8 = 56$ 。下列哪一年不是幸运年份？

A lucky year is one in which at least one date, when written in the form month/day/year, has the following property: the product of the month times the day equals the last two digits of the year. For example, $1956$ is a lucky year because it has the date $7/8/56$ and $7 \times 8 = 56.$ Which of the following is NOT a lucky year?

$1990$

$1991$

$1992$

$1993$

$1994$

答案：E

知识点：因数分类讨论

难度评级：1120

解答：

其他年份都可以： $90 = 9 \times 10$ 、 $91 = 7 \times 13$ 、 $92 = 4 \times 23$ 和 $93 = 3 \times 31$ ，都对应合法的月和日。

对 $1994$ ，最后两位只能分解为 $94 = 2 \times 47$ ，而 $47$ 作为日期太大， $94$ 或 $47$ 作为月份也太大。因此 $1994$ 没有幸运日期。

所以正确答案是 E。

Each of the other years works: $90 = 9 \times 10,$ $91 = 7 \times 13,$ $92 = 4 \times 23,$ and $93 = 3 \times 31,$ each a valid month/day.

For $1994,$ the last two digits factor only as $94 = 2 \times 47,$ and $47$ is too large for a day (and $94$ or $47$ is too large for a month). So $1994$ has no lucky date.

Thus, the correct answer is E .

1995 AMC 8 第 12 题

答案：E

难度评级：1120

解答：

其他年份的第 12 题